The semi-final of the Northern Youth Alliance Cup will be played on Saturday 12th January.
The Shakers progressed in the competition with a penalty shoot-out victory at Preston North End in the quarter-final, after the game finished 1-1.
Bury will travel to Grimsby for the game, which will take place at Cheapside, Waltham DN37 0HT, with kick-off scheduled for 12:00.
The winners of the tie will meet either Scunthorpe United or Wigan Athletic, who also play their semi-final on the same day.